It sounds more like the plot of a Hollywood thriller than a matter to be investigated by a global financial institution: a tale of improbably vast amounts of money and gold smuggled across international borders by a cast of shady characters.

But the International Monetary Fund has been asked to look into the mysterious appearance of more than £11bn in the Turkish treasury, amid allegations that the money was illegally spirited out of Iran.

Three Iranian opposition politicians – including a former foreign minister, Ebrahim Yazdi – have written to the IMF's managing director, Dominique Strauss-Kahn, saying the money belongs to Iran and should be returned.

The money is credited with stabilising Turkey's economy.

But its origins have come under scrutiny after an Iranian businessman, Esmael Safarian-Nasab, claimed he had exported $7.5bn (£4.5bn) in cash and gold bullion worth $11.5bn into Turkey via Germany as part of a joint venture with a Turkish business partner.

Safarian-Nasab's Turkish lawyer, Senol Ozel, said the money and gold were seized by customs officials last October and transferred to government coffers. Some Turkish media outlets claim it had been smuggled across Turkey's border with Iran in trucks.

Turkish media have pointed out that the sums matched an $18.5bn windfall announced late last year by Recep Tayyip Erdogan, Turkey's prime minister.

Economists say it saved the country from seeking a new IMF loan.

Erdogan appeared to attribute the cash to divine intervention. "Turkey's God is great, he injected $18.5bn into the Turkish economy in these hard economic times," he announced.

Officials, including the central bank governor, Dormuz Yilmaz, have dismissed reports that the money was Iranian and the intelligence ministry threatened to prosecute "false" reports.

Some Turkish economists said the money was a dividend from a government amnesty that enabled investors with overseas assets to bring them back without penalty. Ozel has since issued a public apology, saying he was hoodwinked.

Yazdi and his fellow correspondents, Ahmad Sadr Haj-Javadi, a leading member of Iran's Freedom movement, and Ezatollah Sahabi, general secretary of National Religious party wrote to the IMF after Erdogan failed to answer an earlier letter.

"Although the identity of the person who claims to be the owner of this money is mentioned in the attached documents, the real owner is the Iranian nation," they wrote.

Yazdi said he expected Strauss-Kahn to launch an investigation. "The gentleman who claims that money belongs to him says it comes from Iran," Yazdi told the Guardian. "I don't know this man or who he is, but it all seems very strange."